1. Multiple-choice questions (this topic is entitled *** 10, with 3 points for each question and * * * 30 points for each question): Only one of the four alternative answers listed in each question meets the requirements of the topic. Please fill in its code in brackets after the question. Wrong selection, multiple selection or no selection does not score.

(1) "Yes" and "-".

A. Sufficient but not necessary conditions B. Necessary but not sufficient conditions

C. sufficient and necessary conditions D. neither sufficient nor necessary conditions

(2) Let,, and, then this quadrilateral is-()

A. parallelogram B. rectangle C. isosceles trapezoid D. rhombus

(3) It is known that the range of real numbers is-.

A.B. C. D。

(4) The plane with equal distances between four points of the spatial plane is-().

A.4 B.5 C.6 D.7

(5) The inequality for any real number is-().

A.B.

C.D.

(6) Let it be the sum of the top n items in arithmetic progression. If it is, then-().

A.B. C. D。

(7) It is known that the total area of the cone is 3 times of the bottom area, so the central angle of the sector in the side development of the cone is ()

A.B. C. D。

(8) One cube root of a complex number is-().

A.B. C. D。

(9), then the value is ()

A.B. C. D。

(10) is set as two focal points of a hyperbola, where p is a point on the hyperbola and the area is-.

(A) (B) (C) (D)

2. Fill in the blanks (this big question is ***5 small questions, 4 points for each small question, ***20 points): Fill in the answers directly on the horizontal line.

(1 1) The teaching objectives of mathematics classroom teaching should generally include three aspects: process and method.

(12) The Mathematics Curriculum Standard for Ordinary Senior High School (Experiment) holds that students' mathematics learning activities should not be limited to acceptance, recitation, imitation and practice, but should also be advocated, practiced, read and taught by themselves.

(13) If, the maximum value of is.

(14) If four pairs of shoes are randomly selected from five pairs of shoes with different sizes, the probability that these four pairs of shoes can be matched into at least one pair of shoes is.

Inverse matrix of (15) matrix.

Third, the solution (this big question ***5 small questions, 6 points for each small question, ***30 points): the solution should write out the proof process or calculation steps.

(16) How to understand the abstraction of mathematics? How to implement the principle of combining concreteness with abstraction in mathematics teaching?

(17) is a function defined on a real number set, which is the inverse. Student A thinks: "If it doesn't coincide with the image, but it has something in common, then all the things in common are in a straight line." Please judge whether student A's point of view is correct. If it is correct, please give proof; If not, please give a counterexample.

(18) A series whose terms are positive real numbers and the sum of the first few terms is, find the general term.

(19) In the plane rectangular coordinate system, find the enclosed plane area.

(20) Let a function be constant and. If so, the verification is established.

4. Discussion or case design questions (this topic is entitled ***2 small questions, with each small question scoring 10, with a total score of ***20 points): The discussion, analysis or design should have clear viewpoints, clear logic, appropriate evidence and well-founded.

(2 1) Conceptual assimilation is one of the basic ways for students to acquire mathematical concepts. This paper expounds the meaning and psychological process of conceptual assimilation, and illustrates the application of conceptual assimilation in mathematical concept teaching with examples.

(22) Write a lecture on "monotonicity of function".

Reference answers and grading standards

First, multiple-choice questions (this big question * * 10 small questions, 3 points for each small question, 30 points for * * *)

( 1)C (2)B (3)D (4)A (5)A

(6)D (7)A (8)B (9)D ( 10)C

2. Fill in the blanks (5 small questions in this big question, 4 points for each small question, 20 points for * * *)

(1 1) Hands-on practice (2 points) and self-study reading (2 points)

(12) innovative consciousness (2 points), mathematical model (2 points)

( 13) 179

( 14)

( 15)2

Third, answer the question (this big question ***5 small questions, 6 points for each small question, ***30 points)

(16) The choice of mathematics teaching methods is mainly based on the following four aspects.

① According to the purpose of mathematics teaching; ② According to the content of mathematics teaching; (3 points)

③ According to the students' situation; ④ According to the teachers' own literacy conditions. (3 points)

(17) Abstraction is the basic feature of mathematics. In order to study in a relatively pure state, mathematics often ignores other characteristics of objective things and only abstracts its quantitative relationship and spatial form for research. The abstractness of mathematics is mainly manifested in the following aspects: the content of mathematics is highly abstract formal structure and quantitative relationship; Mathematical methods are also highly abstract; The abstraction of mathematics also shows the characteristics of gradual progress; The abstraction of mathematics can reach areas that human perception cannot reach. (3 points)

Concrete is the foundation of mathematical abstraction, and abstraction should be based on concrete. In teaching, we should pay attention to the following aspects: using vivid, vivid, concrete and intuitive realistic materials and teaching language to introduce and clarify new mathematical knowledge; Then give full play to the leading role of teachers in time and guide students to summarize abstract and generalized mathematical concepts and conclusions; Abstract mathematical knowledge and theory should be applied to concrete practice to solve concrete problems and explain concrete phenomena. (3 points)

(18) = (3 points)

,

Therefore ... (3 points)

(19) because, (3 points)

Special solution, the basic solution system of the corresponding homogeneous linear equations,

So the general solution of linear equations is arbitrary constant. (3 points)

(20) Hypothesis comes from the midline theorem.

,

Again, (3 points)

The squares of the two formulas are added, so,

So the hyperbolic equation is. (3 points)

Iv. Discussion or case design questions (this big question is ***2 small questions, each small question 10, and ***20).

(2 1) The teaching of mathematical concepts is generally divided into three stages: introducing concepts to make students perceive concepts and form representations; Through analysis, abstraction and generalization, let students understand and clarify concepts; Make students consolidate and apply concepts through examples and exercises. (3 points)

① Common methods of concept introduction: introducing new concepts based on perceptual materials; Introduce new concepts with the relationship between old and new concepts; Introduce new concepts in the form of "problems"; Introduce new concepts from the process of concept occurrence.

② Clarify the connotation and extension of the concept and correctly express the essential attributes of the concept. Available methods: comparison method and analogy method; Appropriate use of counterexamples; Reasonable use of variants; Form a conceptual system.

③ Pay attention to the consolidation and application of concepts: review in time; Hierarchical structure of concept application; Universality of concept application. (4 points)

Appropriate example analysis. (3 points)

(22) Teaching materials (2 points); Talk about learning (2 points); Speaking of teaching methods (2 points); Talking about the teaching process (2 points); Teaching evaluation (2 points).